Best Known (11, 19, s)-Nets in Base 5
(11, 19, 54)-Net over F5 — Constructive and digital
Digital (11, 19, 54)-net over F5, using
(11, 19, 90)-Net over F5 — Digital
Digital (11, 19, 90)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(519, 90, F5, 8) (dual of [90, 71, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(519, 124, F5, 8) (dual of [124, 105, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(519, 124, F5, 8) (dual of [124, 105, 9]-code), using
(11, 19, 1153)-Net in Base 5 — Upper bound on s
There is no (11, 19, 1154)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 19 081302 960705 > 519 [i]